identify the conic, list the necessary parts and graph: 36(x+1)^2 - 25(y-1)^2 = 900

Question

Identify and list the necessary parts.

Answer 1

The equation is

The conic section is a hyperbola since x²  and y²  have opposite signs.

Divide each side by 900 .

In the above equation x term is positive, then the hyperbola is horizontal.

Compare it to  standard form of horizontal hyperbola is

"a " is the number in the denominator of the positive term

center: (h, k ) Vertices: (h + a, k ), (h - a, k )

Foci: (h + c, k ), (h - c, k )

 Asympototes of hyperbola is

In this case a = 5, b = 6, (h, k) = (-1,1)

Vertices (-1 + 5, 1) ( -1 - 5 , 1) = ( 4 , 1) ( -6 , 1)

Foci: (-1+7.8, 1), ( -1-7.8, 1 ) = (6.8, 1) , (-8.8, 1)

Asympototes of hyperbola is

Graph

Draw the coordinate plane.

Plot the center of hyperbola (-1,1).

To graph the hyperbola go 6 units up and down from center point and 5 units left and right from center point(since a = 5, b = 6.)

Use these points to draw a rectangle .

Draw diagonal lines through the center and the corner of the rectangle. These are asymptotes.

Plot the vertices and foci of hyperbola.

Draw the curves, beginning at each vertex separately, that hug the asymptotes the farther away from the vertices the curve gets.

The graph approaches the asymptotes but never actually touches them.